Homework 03

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CBE 179 - Homework #03

Due Friday, 2014.09.26

As always, state all of the assumptions made in each model and cite your sources.

  1. Calculate and plot the Maxwell-Boltzmann speed and kinetic energy distributions in N₂ at 300K and 400K. Show mean values on the plots. What fraction of the molecules have a velocity of more than 1500 m/s at each temperature?

    the problem originally misstated the velocity of interest as 1500 cm/s; if you correctly calculated the fraction based on this misprint (which should have been essentially 100%) and already handed it in, that's fine; if not, run the integral again with the updated number

  2. Plot mean free path at 300K for air from 1 torr to 760 torr. Use Lennard-Jones estimates for hard sphere radii and collision cross sections.

  3. Estimate mass diffusivity, viscosity, and thermal conductivity for Ar at 300K and 1 atm using mean free path theory. Compare these values with experimentally-determined values.

  4. Consider a cylindrical chamber, 100 cm in diameter and 10 cm high. The chamber initially has a monolayer of liquid water (assume 10^15 molecules per square centimeter) on the interior walls. If all this water is released as vapor at 300K, how much does the pressure rise in the chamber?

  5. Assuming the vacuum chamber in problem #04 has a 1mm diameter hole connecting it to an adjacent chamber maintained at 10^-10 torr, how long would it take to reduce the pressure from the water vapor in the first chamber from 1 torr to 10^-3 torr?

  6. If the chamber in problem #04 has, instead of a small hole, a very cold (e.g. liquid nitrogen-cooled) surface, this can also act as a kind of pump since the water vapor will condense on every surface collision. How long would it take to reduce the pressure from the water vapor from 1 torr to 10^-3 torr if the cold plate is 100cm in diameter?

  7. Why is hydrogen a difficult gas to pump with a turbomolecular pump?

  8. While modern processing techniques enrich fissile uranium from naturally-occurring isotopic mixtures using a gas centrifuge, the Manhattan Project (1942-1946) accomplished this separation with gas diffusion‒based techniques. From the physics of gaseous uranium, how is this separation achieved? What is the best-case enrichment achievable with a gas diffusion cascade system of n stages?

Suggested Reading

Wikipedia: Kinetic Gas Theory

Pfeiffer Vacuum: Working with Turbopumps

Sage Math: Maxwell-Boltzmann Distribution